# Homework Help: Inverse Laplace transform

1. Oct 16, 2006

### Benny

Hi I'm having problems find the inverse Laplace transform of $$\frac{s}{{\left( {s + 4} \right)^4 }}$$ via a table/look up method.

In another question part I found the inverse Laplace transform of (s+4)^-4 by considering $$\frac{{d^3 }}{{db^3 }}\left[ {\left( {s + b} \right)^{ - 1} } \right]$$ so that the problem essentially reduced to finding the inverse Laplace transform of 1/(s+b). After that I just set b = 4 to get the answer.

But I can't think of a way to do this one (the one in the first sentence of this post). I have $$L^{ - 1} \left\{ {\frac{1}{{\left( {s + 4} \right)^4 }};s \to t} \right\} = \frac{{t^3 }}{6}e^{ - 2t}$$ but I don't see a way to use it to find the inverse Laplace transform of s(s+4)^-4. Can someone please help me out? Thanks.